A moving wave patterns the cone photoreceptor mosaic array in the zebrafish retina

In this paper, we describe the embryonic origin and patterning of the planar mosaic array of cone photoreceptor spectral subtypes in the zebrafish retina. A discussion of possible molecular mechanisms that might generate the cone mosaic array considers but discards a model that accounts for formation of neuronal mosaics in the inner retina and discusses limitations of mathematical simulations that reproduce the zebrafish cone mosaic pattern. The formation and organization of photoreceptors in the ommatidia of the compound eye of Drosophila is compared with similar features in the developing zebrafish cone mosaic, and a model is proposed that invokes spatiotemporally coordinated cell-cell interactions among cone progenitors to determine the identity and positioning of cone spectral subtypes.     

Outer retinal fine structure of the garfish Belone belone (L.) (Belonidae, Teleostei) during light and dark adaptation – photoreceptors, cone patterns and densities

In the present EM study, we investigate the retina of Belone belone , a visually-orientated marine predator living close to the water surface. In the duplex retina, four morphologically different cone types are observed: unequal and equal double cones, long single cones and triple cones. In the light-adapted state, five different cone patterns occur: row, twisted row, square, pentagonal and hexagonal patterns. High double cone densities are found ventro-nasally, ventro-temporally and dorso-temporally. Throughout the retina the double cone/single cone ratio is 2 : 1, in the ventral part, however, a 1 : 1 ratio occurs. In the vitreous body we found a curtain-like intraocular septum dividing the retina into two morphologically different regions. In most areas of the dark-adapted retina the cone patterns are absent at the ellipsoid level, with long single cones standing more vitreally in the light path than double cones. The mosaics are retained, however, in the outer nuclear layer. Typical dark adaptation, i.e. the retinomotor movements of the retinal pigment epithelium and photoreceptors in response to the dark adaptation (light change) is not present in the peripheral ventral and parts of the central ventral area. In both regions we found a twisted row pattern of cones having a vitreal position. The findings are discussed with respect to the photic habitat and feeding habits of this species.     

Changes in the Visual Cell Layer of the Duplex Retina During Growth of the Eye of a Deep-sea Teleost,Gempylus serpens Cuvier, 1829

Ontogenetic changes in the visual cell layer of the duplex retina during growth of the eye of the deep-sea teleost Gempylus serpens, the snake mackerel, are illustrated by comparing the retina of a small specimen with that of a previously studied adult fish. The small specimen has tightly packed cones spanning the whole width of the visual cell layer and small rods situated in its vitread part. Over most of the retina the cone population consists of single cones arranged in a very regular hexagonal mosaic. The temporalmost retina has a cone population consisting mainly of twin cones arranged in meridional rows. Growth of the eye is associated with an increase in the thickness of the visual cell layer and the density of rods and a total elimination of the densely packed single cones, the retina of the adult fish possessing only a temporally located population of double cones. The radical differences between the retina of the small and adult snake mackerel are probably associated with the different light regimes encountered by small and large specimens.     

Restoration of cone vision in a mouse model of achromatopsia

Loss of cone function in the central retina is a pivotal event in the development of severe vision impairment for many prevalent blinding diseases. Complete achromatopsia is a genetic defect resulting in cone vision loss in 1 in 30,000 individuals. Using adeno-associated virus (AAV) gene therapy, we show that it is possible to target cones and rescue both the cone-mediated electroretinogram response and visual acuity in the Gnat2 ( cpfl3 ) mouse model of achromatopsia.     

Regional variations in the outer retina of atherinomorpha (Beloniformes,Atheriniformes, Cyprinodontiformes: Teleostei): photoreceptors,cone patterns,and cone densities

The outer retinae of adults of 13 atherinomorph species, representing nine different families, were examined by both light and electron microscopy. The retinae were investigated with respect to photoreceptor types, cone densities, and cone patterns. All data were composed to eye maps. This procedure allows an interspecific comparison of the regional differences within the outer retina among these shallow-water fish. Furthermore, for a more detailed pattern analysis nitro-blue tetrazolium chloride- (NBT)-stainings in the retina of Melanotaenia maccullochi are presented. Apart from rods, eight morphologically different cone types could be identified: short, intermediate, and long single cones, double cones (equal and unequal), triple cones (triangular and linear), and in Ameca splendens one quadruple cone. Dimensions and occurrence of photoreceptors vary among the respective species and within the retinal regions. In the light-adapted state, the cones are arranged in highly ordered mosaics. Five different cone tessellation types were found: row patterns, twisted row patterns, square patterns, pentagonal patterns, and, exclusively in Belone belone, a hexagonal pattern. In Melanotaenia maccullochi the different spectral photoreceptor classes correspond well with the distribution of morphological photoreceptor classes within the mosaic. Double cone density maxima together with a highly ordered cone arrangement usually occur in the nasal and/or ventral to ventrotemporal retina. In most of the species that were examined these high-density regions are presumed to process visual stimuli from the assumed main directions of vision, which mainly depend on feeding behavior and predator pressure. Our findings are discussed with respect to the variable behavioral and visual ecology and phylogeny of the respective species.     

Mosaic model for color vision

Color vision in man is based upon three different cone types, which are quite likely arranged in a semi-ordered array in the retina. The model proposes that this ordering is an inherent part of the genetic code that sets up the color vision mechanism, and that the specification for each cone type (red, green or blue) also includes a specification for its place in the larger structure of which it is a part. One possible positional mosaic for the three cone types is proposed, together with its degeneracies into anomalous (red-green) color mechanisms. Assuming only one fixed probability for a degenerate transition, the population frequencies for color anomalies predicted from the model agree closely with the observed frequencies.     

Clathrin lattice reorganization: theoretical considerations

We wish to postulate a mechanism by which flat hexagonal lattices of clathrin trimers transform into coated pits. Using an established model for packing trimers into lattices, we explored the assembly process by single addition of trimers to form polygons. Subject to favorable conditions, removal of a single trimer from a hexagon could lead to the formation of a pentagon. Elimination of trimers from polygonal sheets can occur either at the center of the network or at the edges. Removal of a trimer from the center of these adjacent polygons, "hub transformation," is possible in very few instances, whereas removal from the edges of a polygonal sheet, "fringe transformation," is possible in a host of cases. These hypothetical constructs can be used effectively to explain intermediate structures actually observed in flat hexagonal lattices. The geometry of a purely hexagonal lattice seems to dictate that the first step in transformation must be a "fringe transformation," which then will allow subsequent "hub transformation" to take place leading to the introduction of pentagons into the center of the lattice and ultimately to the curvature of the clathrin lattice.     

Increasing Biomass Production on Limited Land Area Through an Optimal Planting Arrangement

Planting density is a primary consideration in silviculture; however, planting arrangement is often ignored. Most, if not all, forest plantations are arranged in rectangular or square lattices (i.e., grids). Using a simple mathematical model, we investigate the potential influence of planting arrangement on planting density, biomass yield, and rotation period by assuming that efficiently arranging trees is similar to packing congruent circles on a plane. The hexagonal lattice achieves the densest circle packing on a plane; therefore, a hexagonal or triangular lattice arrangement of stems provides the highest planting density for a given spacing. Using packing density to quantify arrangement efficiency, tree crowns in a hexagonal lattice fill approximately 90.7% of available area at initial canopy contact, while tree crowns in a square lattice fill approximately 78.5% of available area at initial canopy contact. The hexagonal lattice permits about a 15% higher density than the square lattice, which allows canopy closure to occur earlier without any change in individual tree growth. Short rotation woody crop (SRWC) systems are excellent candidates under the model’s assumptions of level stand with even-age monoculture. If belowground resources are non-limiting, a hexagonal lattice arrangement shortens rotation period and thus optimizes the biomass yield per land area over time. Higher productivity over time is central to sustainable and efficient use of limited area for bioenergy and biomass products.     

Protein folding on the hexagonal lattice in the HP model

In this paper, we introduce the 2D hexagonal lattice as a biologically meaningful alternative to the standard square lattice for the study of protein folding in the HP model. We show that the hexagonal lattice alleviates the "sharp turn" problem and models certain aspects of the protein secondary structure more realistically. We present a 1/6-approximation and a clustering heuristic for protein folding on the hexagonal lattice. In addition to these two algorithms, we also implement a Monte Carlo Metropolis algorithm and a branch-and-bound partial enumeration algorithm, and conduct experiments to compare their effectiveness.     

Formation of cone mosaic of zebrafish retina.

In the zebrafish retina, four types of cone photoreceptor cells (or cones) with different sensitive frequencies are arranged in a regular pattern, named "cone mosaic". A pair of small cones, one sensitive to red and the other sensitive to green, is in close contact and forms a "double cone". In addition, there are two kinds of single cones, sensitive to blue and to UV, respectively. We study characteristics of cell-differentiation rules that realize stable formation of cone mosaic. Assumptions are: undifferentiated cells are arranged in a regular square lattice, and they are one of the three types (B, U, and D cells). A D cell has two parts (G and R-parts) and takes one of the four directions. The cells change their cell type and orientation following a continuous-time Markovian chain. The state transtion occurs faster if it increases the stabilities of the focal cell, in which the stability is the sum of affinities with neighboring cells. After the transient period, the system may reach a stable pattern (pre-pattern). The pattern becomes fixed later when the cells are fully differentiated in which B cells, U cells, and D cells become blue-sensitive, UV-sensitive, and double cones, respectively. We search for the combinations of affinities between cell states that can generate the same cone mosaic patterns as in zerbrafish retina. Successful transition rules give (1) zero or small affinity with the pairs of cell states that are absent in the zebrafish cone mosaic (lambda(UR), lambda(BG)and the contact of two cells of the same type); (2) a large affinity between a part of D cells and a non-D cell (lambda(UG)and lambda(BR)); and (3) a positive affinity of an intermediate magnitude between two non-D cells (lambda(BU)) and between two parts of D cells (lambda(GR)). The latter should be of a magnitude of about 60-90% of the former. The time needed to form a regular pattern increases with the lattice size if all the cells start pre-pattern formation simultaneously. However, the convergence time is shortened considerably if the pre-pattern formation occurs only in a narrow band of morphogenetic cell layer that sweeps from one end of the lattice to the other.     

Stability of the hexagonal lattice structure formed by an R-form lipopolysaccharide of Klebsiella: decrease in the stability by electrodialysis and recovery by addition of the magnesium

The R-form lipopolysaccharide (LPS) from Klebsiella strain LEN-111 (O3-:K1-) forms a hexagonal lattice structure with a lattice constant of 14 to 15 nm when it is precipitated by addition of two volumes of 10 mM MgCl2-ethanol. When the LPS was suspended in various buffers (50 mM) at pH 2 to 12 for 24 hr at 4 C, at pH 2 and 3 pits of the hexagonal lattice structure markedly disappeared, at pH 4 to 8.5 the lattice structure was stable, and at pH 9 to 12 it tended to loosen somewhat. The LPS from which cations were removed by electrodialysis retained the ability of hexagonal assembly, although the lattice constant of the hexagonal lattice of the electrodialyzed LPS was large. The lattice structure of the electrodialyzed LPS was much more labile than that of the non-electrodialyzed LPS at alkaline pH levels and the former was completely disintegrated into ribbon-like structures when the LPS was suspended in 50 mM Tris buffer at pH 7.7 or higher. However, the electrodialyzed LPS formed a hexagonal lattice structure in Tris buffer at pH 8.5 containing 0.1 to 100 mM MgCl2. The lattice constants of the hexagonal lattice formed by the electrodialyzed LPS at 10 or 100 mM MgCl2 were very similar to that of the lattice of the non-electrodialyzed LPS. From these results it is concluded that the lability of the hexagonal lattice structure of the electrodialyzed LPS at alkaline conditions is due to removal of Mg2+ by electrodialysis.     

The photoreceptor populations in the retina of the greater horseshoe bat Rhinolophus ferrumequinum

Recently, we reported the existence of AII "rod" amacrine cells in the retina of the greater horseshoe bat Rhinolophus ferrumequinum (Jeon et al., 2007). In order to enhance our understanding of bat vision, in the present study, we report on a quantitative analysis of cone and rod photoreceptors. The average cone density was 9,535 cells/mm2, giving a total number of cones of 33,538 cells/retina. The average rod density was 368,891 cells/mm2, giving a total number of rods of 1,303,517 cells. On average, the total populations of rods were 97.49%, and cones were 2.51% of all the photoreceptors. Rod: cone ratios ranged from 33.85:1 centrally to 42.26:1 peripherally, with a mean ratio of 38.96:1. The average regularity index of the cone mosaic in bat retina was 3.04. The present results confirm the greater horseshoe bat retina to be strongly rod-dominated. The rod-dominated retina, with the existence of AII cells discovered in our previous study, strongly suggests that the greater horseshoe bat retina has a functional scotopic property of vision. However, the existence of cone cells also suggests that the bat retina has a functional photopic property of vision.     

Modelling of the vertebrate visual system 3. topological analysis of the cone mosaic

Spatial organization of the cone mosaic of the generalized vertebrate retina consists of rows of red and green cones alternating with rows of blue and blank cones. Cone inputs to retinal elements are defined spatially by red and green unit hexagons. Topological analysis entails determining for each cone in the mosaic the number of each cone type present in the unit hexagon which the activated cone can influence via electrical coupling between cones and/or stray light. Only weighted inputs in one-half of a sextant of the unit hexagon need be designated, since all other weighted inputs can be determined by rules giving systematic transformations of all cone types from one sextant to another: these rules arise from symmetries of the cone mosaic. Four retinal types are possible depending on replacement of blank cones by specific cone types; three cone-dominant retinas, where all blank cones are replaced by a specific cone type, and two forms of a trichromatic retina, where blank cones are replaced by equal numbers of red and green cones. The weighted input is the sum of individual cone type contributions and depends on the number of each cone type in the unit hexagon which can influence the cone in question. Weighted inputs for cone-dominant retinas are readily found by replacing blank cones with the proper cone type, while weighted inputs for trichromatic retinas require use of a specified cone mosaic to determine extra red and green cones. Receptive field size of post-cone elements as well as overlap of the center and surround fields of annular organized receptive fields of retinal elements increased with increasing values for attenuation factors.     

Avian Cone Photoreceptors Tile the Retina as Five Independent,Self-Organizing Mosaics

The avian retina possesses one of the most sophisticated cone photoreceptor systems among vertebrates. Birds have five types of cones including four single cones, which support tetrachromatic color vision and a double cone, which is thought to mediate achromatic motion perception. Despite this richness, very little is known about the spatial organization of avian cones and its adaptive significance. Here we show that the five cone types of the chicken independently tile the retina as highly ordered mosaics with a characteristic spacing between cones of the same type. Measures of topological order indicate that double cones are more highly ordered than single cones, possibly reflecting their posited role in motion detection. Although cones show spacing interactions that are cell type-specific, all cone types use the same density-dependent yardstick to measure intercone distance. We propose a simple developmental model that can account for these observations. We also show that a single parameter, the global regularity index, defines the regularity of all five cone mosaics. Lastly, we demonstrate similar cone distributions in three additional avian species, suggesting that these patterning principles are universal among birds. Since regular photoreceptor spacing is critical for uniform sampling of visual space, the cone mosaics of the avian retina represent an elegant example of the emergence of adaptive global patterning secondary to simple local interactions between individual photoreceptors. Our results indicate that the evolutionary pressures that gave rise to the avian retina''s various adaptations for enhanced color discrimination also acted to fine-tune its spatial sampling of color and luminance.     

ENDOGENOUS LEVELS OF NEUROTRANSMITTER CANDIDATES IN PHOTORECEPTOR CELLS OF THE TURTLE RETINA

The neurotransmitter used by vertebrate photoreceptors has not been identified, although aspartic acid, glutamic acid and acetylcholine have all been suggested as possible candidates. In the present study, we have measured the endogenous levels of these substances in isolated photoreceptors of the turtle retina. Fractions containing over 80% of identified photoreceptors were obtained by enzymatic dissociation of the retina followed by velocity sedimentation at unit gravity. The endogenous levels of free amino acids in these fractions were measured by amino acid analysis and the ACh content was measured by a radiochemical assay. In addition, identified photoreceptors were drawn into a micropipet individually under visual observation and their ACh content was determined. Our results show that while the concentrations of free aspartic acid and glutamic acid in isolated photoreceptors are similar to those found in the retina, the concentration of ACh in cone photoreceptors (0.1–0.2 mM) is 2- to 3-fold higher than that in the turtle retina. This result combined with the findings of others suggests that turtle cone photoreceptors may be cholinergic     

Suppression of cone signal in the dark-adapted frog retina as indicated by the electroretinogram.

Electroretinogram (ERG) cone acitvity is depressed in the dark-adapted frog retina. The strength of this effect is examined over a large range of flash energy, for 618 nm flashes extending up to about 4 log10 units above the "threshold" (10-25 micron V b-wave) of the cone ERG "released" in the early stage of rapid dark-adaptation (RDA). Cone signal depression is remarkably strong over this flash energy range. The cone ERG is practically absent for flashes up to about I log unit above cone RDA threshold. For stronger flashes, the suppression becomes time-dependent, that is, cone signal is very small for the first few hundred msec. after the flash, cone intrusion then becoming detectable. The results suggest that the cone suppression phenomena arises distally in the retina, probably near the receptor layer, and that cone signal intrusion a few hundred msec. after a strong flash may be due to light-adaptation of rods by the flash itself.     

Duplex Retina in the Mesopelagic Deep-Sea Teleost Lestidiops affinis (Ege, 1930)

The eye of the deep-sea teleost Lestidiops affinis has been examined primarily by light microscopy and found to possess a duplex retina consisting of two main divisions, a pure-cone and a pure-rod region, with a narrow zone of transition, possessing both cones and rods, joining the two. The pure-cone region is located in the temporal (caudal) part of the retina subserving binocular vision in the rostral direction. It has an area temporalis retinae with particularly long and densely packed single cones arranged in a regular hexagonal mosaic. Joined (double or twin) cones have not been recognized with certainty in the pure-cone region. The pure-rod region, comprising the larger part of the retina, contains rods grouped in bundles separated by retinal pigment epithelium (RPE) processes with pigmented cores. The synaptic endings of the rods are arranged in separate clusters in the outer plexiform layer, there being apparently a separate rod pedicle cluster beneath (vitread to) each rod bundle. Structural comparisons with certain other deep-sea teleosts suggest the likely presence of a retinal tapetum in L. affinis, i.e. each single cone or rod bundle is situated in a reflecting pit formed by the RPE, with a discrete reflector apposed to the tip of each cone outer segment and the tips of the outer segments of each square-cut rod bundle.     

Photoreceptor topography in the duplex retina of the paddlefish (Polyodon spathula)

Retinal whole-mount preparations from the eyes of the North American paddlefish, Polyodon spathula, were examined with a combination of bright field and differential interference contrast microscopy. The entire retina was mapped and population counts of rod and cone photoreceptors were made at regular intervals throughout the retina. The retina is dominated by rods, but a significant percentage (ca. 38%) of the photoreceptors are cones. Mean cone packing density for the entire retina is 6,402+/-1,216 cones/mm2. There is a small (16%) but statistically significant difference between cone packing density in the dorsal retina (6,674+/-1,168 cones/mm2) and the ventral retina (5,745+/-1,076 cones/mm2). There is no region of unusually high cone concentration that might be construed as a fovea or a visual streak. Mean rod packing density for the entire retina is 10,271+/-1,205 rods/mm2. Except in the far periphery, where rods are less numerous, the density of rods is fairly uniform throughout the retina. The data are discussed with regard to paddlefish habitat and behavior.     

Relationship between Mg2(+)-induced hexagonal assembly of R-form lipopolysaccharides and chemical structure of their R-cores

The relationship between formation of the Mg2(+)-induced hexagonal lattice structure by R-form lipopolysaccharides (LPS) and chemical structure of their R-cores was investigated using different kinds of R-form LPS from a series of mutants of Salmonella minnesota or S. typhimurium. The optimal experimental condition for formation of the hexagonal lattice structure was to suspend LPS preparations, from which cationic material was removed by electrodialysis, in 50 mM tris (hydroxymethyl) aminomethane buffer at pH 8.5 containing 10 mM MgCl2. Under this experimental condition, Rb1 LPS formed the hexagonal lattice structure with the lattice constant of 14.0 +/- 0.2 nm. Ra LPS, which possesses the full length of R-core, also formed the hexagonal lattice structure but its lattice constant was larger (18.1 +/- 0.2 nm) than that of Rb1 LPS (the lattice structure by Ra LPS was looser than that by Rb1 LPS). All the other R-form LPS preparations tested, RcP+, PcP-, Rd1P-, and Re LPS, whose R-cores are shorter than that of Rb1 LPS, did not form the hexagonal lattice structure, but formed membranous structures showing various shapes which consisted of multiple bilayer structures. Failure to form the hexagonal lattice structure was the common feature of these kinds of R-form LPS irrespective of temperature at which the LPS suspensions in 10 mM MgCl2-50 mM Tris buffer were incubated. From the results of the present study it was concluded that capability of R-form LPS to form the hexagonal lattice structure has a close correlation with the chemical structure of their R-cores.